Kinetic data for modeling the dynamics of the enzymes involved in animal fatty acid synthesis.

The synthesis and modification of fatty acids (FAs) from carbohydrates are paramount for the production of lipids. Simultaneously, lipids are pivotal energy storage in human health. They are associated with various metabolic diseases and their production pathways are for instance candidate therapeutic targets for cancer treatments. The fatty acid de novo synthesis (FADNS) occurs in the cytoplasm, while the microsomal modification of fatty acids (MMFA) happens at the surface of the endoplasmic reticulum (ER). The kinetics and regulation of these complex processes involve several enzymes. In mammals, the main ones are the acetyl-CoA carboxylase (ACC), the fatty acid synthase (FAS), the very-long-chain fatty acid elongases (ELOVL 1-7), and the desaturases (delta family). Their mechanisms and expression in different organs have been studied for more than 50 years. However, modeling them in the context of complex metabolic pathways is still a challenge. Distinct modeling approaches can be implemented. Here, we focus on dynamic modeling using ordinary differential equations (ODEs) based on kinetic rate laws. This requires a combination of knowledge on the enzymatic mechanisms and their kinetics, as well as the interactions between the metabolites, and between enzymes and metabolites. In the present review, after recalling the modeling framework, we support the development of such a mathematical approach by reviewing the available kinetic information of the enzymes involved.

Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models.

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis.